Space and time are apparently fundamental in the universe. The origins and the nature of space and time has fascinated humans for millenniums with no comprehensive understanding of why and how they are so. That space and time are so ubiquitous but they are so elusive to elucidate, is an ongoing challenge to philosophers and scientists, even in the 21st century.

Why is it so difficult to do so?

Let’s explore this intractable problem by first defining what is space and time.

Time is a dimension in which events can be ordered from the past through the present into the future, and also the measure of durations of events and the intervals between them.

The above definition of time is problematic as the words “events”, “past”, “present”, “future”, “duration” and “intervals” are all temporal descriptions (which are related to time itself) and hence the definition of time as such, is circular.

So, how can time be defined without circularity?

We can try to define time wrt change (the process of becoming different). However, if we do that, it implies if there is no change, there is no time which is very odd indeed, although it is consistent with the taoist philosophical concept that change is universal in the universe which entails time is also universal in the universe, if time is related to change.

OTOH, the other apparently seemingly strange consequence of associating time with change is that there is variable time for variable change, i.e. there is no fixed duration of time as measured by clocks. However, we can contend that clocks do not measure time per se as all clocks depend on the constant motion or oscillation of some entity (from pendulums to Cesium atoms) which gives us the illusion/delusion of the regular passing of time.

In physics, spacetime (also space–time, space time or space–time continuum) is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as existing in three dimensions and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions.

Since spacetime is a mathematical model and not necessarily as such in reality, it is prudent to consider spacetime as just that.

No account of what is space and time in general relativity or quantum mechanics:

If nothing else, they say, neither of the two great pillars of modern physics — general relativity, which describes gravity as a curvature of space and time, and quantum mechanics, which governs the atomic realm — gives any account for the existence of space and time. Neither does string theory, which describes elementary threads of energy.

Gravity as thermodynamics without bending space-time?

From that, he found, the mathematics yielded Einstein’s equations of general relativity — but using only thermodynamic concepts, not the idea of bending space-time.

“This seemed to say something deep about the origins of gravity,” says Jacobson. In particular, the laws of thermodynamics are statistical in nature — a macroscopic average over the motions of myriad atoms and molecules — so his result suggested that gravity is also statistical, a macroscopic approximation to the unseen constituents of space and time.

Causality, causal dynamical triangulations and discrete space:

But, like Sorkin, Loll and her colleagues found that adding causality changed everything. After all, says Loll, the dimension of time is not quite like the three dimensions of space. “We cannot travel back and forth in time,” she says. So the team changed its simulations to ensure that effects could not come before their cause — and found that the space-time chunks started consistently assembling themselves into smooth four-dimensional universes with properties similar to our own

Quantum entanglement and space-time are the same thing?

So, in effect, Van Raamsdonk concluded, the three-dimensional universe is being held together by quantum entanglement on the boundary — which means that in some sense, quantum entanglement and space-time are the same thing.

Or, as Maldacena puts it: “This suggests that quantum is the most fundamental, and space-time emerges from it.”

This is the state of investigations into the origins and nature of space and time at present.

The Universe is commonly defined as the totality of existence, including planets, stars, galaxies, the contents of intergalactic space, and all matter and energy. Similar terms include the cosmos, the world and nature.

Is the universe finite or infinite?

According to general relativity, space can expand faster than the speed of light, although we can view only a small portion of the Universe due to the limitation imposed by light speed. Since we cannot observe space beyond the limitations of light (or any electromagnetic radiation), it is uncertain whether the size of the Universe is finite or infinite.

Bold added by me.

Size of the universe:

The size of the Universe is unknown; it may be infinite. The region visible from Earth (the observable universe) is a sphere with a radius of about 46 billion light years, based on where the expansion of space has taken the most distant objects observed.

Bold added by me.

Structure of the universe:

The Universe appears to have a smooth space-time continuum consisting of three spatial dimensions and one temporal (time) dimension. On the average, space is observed to be very nearly flat (close to zero curvature), meaning that Euclidean geometry is experimentally true with high accuracy throughout most of the Universe.

Bold added by me.

The implication is that the expanding dynamic universe is probably infinite wrt space.

Creation of the universe?

In other stories, the Universe emanates from fundamental principles, such as Brahman and Prakrti, the creation myth of the Serers, or the yin and yang of the Tao.

Philosophical models:

The theory of temporal finitism was inspired by the doctrine of Creation shared by the three Abrahamic religions: Judaism, Christianity and Islam. The Christian philosopher, John Philoponus, presented the philosophical arguments against the ancient Greek notion of an infinite past and future.

The second argument, the “argument from the impossibility of completing an actual infinite by successive addition”, states:

“An actual infinite cannot be completed by successive addition.”
“The temporal series of past events has been completed by successive addition.”
“therefore The temporal series of past events cannot be an actual infinite.”

The two arguments start from the doubtful premises that either an actual infinity cannot exist or time is finite.

Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin infinitas, which can be translated as “unboundedness”, itself calqued from the Greek word apeiros, meaning “endless”.

The first argument begs the question whereas the second argument unjustifiably assume that time is finite. Thus, both arguments are fundamentally flawed.

Thus, if space and time is infinite, as “something without any limit”, “unboundedness” and “endless” it also implies they are also “beginningless”.

From the same wiki on infinity:

Cosmology:

If, on the other hand, the universe were not curved like a sphere but had a flat topology, it could be both unbounded and infinite. The curvature of the universe can be measured through multipole moments in the spectrum of the cosmic background radiation. As to date, analysis of the radiation patterns recorded by the WMAP spacecraft hints that the universe has a flat topology. This would be consistent with an infinite physical universe.

Bold added by me.

If space is infinite, and if time is related to change wrt space, then it implies time is also infinite.

However, we are still clueless wrt whether space or time is more fundamental or are both inherent (to preserve causality), in the universe?

The above definition of time is problematic as the words “events”, “past”, “present”, “future”, “duration” and “intervals” are all temporal descriptions (which are related to time itself) and hence the definition of time as such, is circular.

So, how can time be defined without circularity?

Why should it be defined without circularity?

A scientific theory and e.g. an argumentative chain are not the same. In an argumentative chain one tries to establish the truth of a proposition by basing them on other, for all people evident, truths. So circularity in a logical argumentation is a fallacy. However in science we ‘only’ need a theory that is self-consistent and corresponds with observable facts. It does not matter when definitions are circular, as long as we can assign observed values to parameters in our theory and can predict other future observations correctly with it. Removing circularity can be an aim in order to reduce the number of dependent variables in a theory, but it is not an absolute methodological necessity: a scientific theory is not wrong because it contains circularities.

This error is often made by (would-be) philosophers who have no experience in any (hard) science themselves.

A circular definition is one that uses the term(s) being defined as a part of the definition or assumes a prior understanding of the term being defined. Either the audience must already know the meaning of the key term(s), or the definition is deficient in including the term(s) to be defined in the definition itself. Such definitions lead to a need for additional information that motivated someone to look at the definition in the first place and, thus, violate the principle of providing new or useful information.

Time is not easy to define (because we do not know, fundamentally, what is time) and hence the circularity of temporal terms, in the wiki on time:

Time has long been a major subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars

Bold added by me.

My proposal was to define time wrt change to avoid circularity.

A scientific theory and e.g. an argumentative chain are not the same. In an argumentative chain one tries to establish the truth of a proposition by basing them on other, for all people evident, truths. So circularity in a logical argumentation is a fallacy. However in science we ‘only’ need a theory that is self-consistent and corresponds with observable facts. It does not matter when definitions are circular, as long as we can assign observed values to parameters in our theory and can predict other future observations correctly with it. Removing circularity can be an aim in order to reduce the number of dependent variables in a theory, but it is not an absolute methodological necessity: a scientific theory is not wrong because it contains circularities.

Did I mention a fallacy and why should you go off on a tangent, GdB?

Begging the question i.e. circular logic, is a fallacy but not necessarily for a circular definition.

Begging the question (Latin: petitio principii, “assuming the initial point”) is a type of informal fallacy in which an implicit premise would directly entail the conclusion; in other words, basing a conclusion on an assumption that is as much in need of proof or demonstration as the conclusion itself.